Financial instruments, system, and exchanges (financial, stock, option and commodity) based upon realized volatility

ABSTRACT

A financial instrument, exchange, and method based upon the volatility in the price of an underlying. Such volatility contracts have a creation date, a term expiring at an expiration date, and a settlement price at the expiration date defined as “Svol”, under the formula: Svol=f{Rt1,Rt2,Rt3, . . . , Rtn}, wherein: Svol≧0, n&gt;1, t=each of a series of observation points from 1 to “n”; Rt=return of the underlying based upon each of the observation points in time “tn”; and n=total number of observations within the term. The term is selected from the group consisting of days, months, quarters and years. The settlement price is annualized based upon an approximate total number of periods in a calendar year. Rt is selected from the group consisting of: R t = ln ⁡ ( M t M t - 1 ) ⁢ ⁢ and ⁢ ⁢ R t = ( M t - M t - 1 M t - 1 ) wherein: Mt=mark-to-market price at time “t”; and Mt−1=mark-to-market price at the time immediately prior to time “t”, at time “t−1”. The settlement price is determined in accordance with the following formula: S vol = P n ⁢ ∑ n t = 1 ⁢ R t 2 ⁢ ⁢ or ⁢ ⁢ S vol = P n - 1 ⁢ ∑ n t = 1 ⁢ ( R t - R _ ) 2 wherein: P=approximate number of trading periods in a calendar year, and each observation point “t” is taken at the same time in each trading period, and R=mean of all Rt&#39;s.

FIELD OF THE INVENTION

The present invention relates to the field of financial and negotiableinstruments and exchanges that trade in such instruments, and morespecifically to standardized financial instruments that aremarket-priced, purchased and sold, and that settle at a price that isbased solely on the volatility of the underlying over a certainpredefined period of time.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. The copyright owner has noobjection to the reproduction by anyone of the patent document or patentdisclosure as it appears in the U.S. Patent and Trademark Office filesor records for the purposes inherent in U.S. Patent law, but reservesall other rights in connection with duplication and copying.

BACKGROUND OF THE INVENTION

Numerous financial and negotiable instruments exist to facilitate theexchange of goods and services. Others have been created to minimize orexchange risks inherent in underlying transactions. Many have beenstandardized and trade on regulated exchanges. For example, a promissorynote promises the payment of money over a term and is typically employedto facilitate the acquisition of goods. If terms are standardized, thenfutures and options could be created to assist in transferring the riskin this and similar transactions. By definition, “instruments” provide“formal expression to a legal act or agreement, for the purpose ofcreating, securing, modifying or terminating a right.” See Black's LawDictionary, West, Revised 4^(th) Edition, 1968.

Once an instrument is created, it can be purchased and sold. Sinceinstruments have a term, one can bargain in the price. The instrumentitself can be purchased and sold over time, and one can “observe” aprice at any given point in time (if the instrument is standardized andis listed on a regulated or non-regulated exchange). The fluctuationsbetween observations can be measured with a statistical standarddeviation formula known as “volatility.” The instrument itself can becalled an “underlying,” when there are instruments that derive theirvalue from it. Volatility is an absolute value, since it is the amountof change, rather than the upward or downward direction of that change.

Volatility between observations can be determined after the observationshave occurred. Such historical viewing can provide the data necessaryfor a calculation of historical volatility. Conceptually, the risksassociated with future volatility can be the subject of a bargain,themselves being purchased and sold, and thereby assisting theassumption or minimization of risk. However, prior to the inventionherein, there has been no effective standardized mechanism by which atradable instrument captures the future (realized) volatility of anunderlying, in which the instrument has a term, observations during thatterm, an annualized figure, and wherein final settlement of such aninstrument can coincide with the settlement of the options on theunderlying.

Risk is a key element in every business and financial decision, and itspresence, dictated by the unknown that the future might bring, has beenthe basis by which the financial markets have prospered. Participants inthese markets have been able to reduce or increase their risk by tradinginstruments that capture price changes in existing markets for suchtrading. However, participants have heretofore been unable to obtainexposure to changes in the level of that risk by way of standardizedinstruments.

Contrary to the assumption of popular option-pricing models, changes inmarket risks can be dramatic. The Bank of International Settlementsestimates that $13 trillion of notional over-the-counter (“OTC”) optioncontracts were outstanding as of June 1999—a twenty times increase fromsix and one-half years ago. While investment banks seek to delta-hedgethis exposure, which effectively neutralizes the directional risk (i.e.,whether the contract is trading at a higher or lower price), this stillleaves behind significant volatility exposure (that is the amount andspeed of change). The same concept holds true for option market makers.

Multi-national corporations, looking closely, may find that in additionto directional risk they really have large amounts of volatility risk.Hedge fund managers and commodity trading advisors could easily use anew asset class to base new, uncorrelated trading programs. And,exchanges are always looking for new products that could enhance volume.

Formulas for calculating volatility, and mechanisms for swapping orminimizing volatility have been considered. For example, Brenner, M. andDan Galai (1989), “New Financial Instruments for Hedging Changes inVolatility,” Financial Analysts Journal (July-August), pp. 61-65,proposes a so-called “Sigma Index.” Yet, this reference fails toindicate the mechanism for constructing such an index other than bystating that “[i]t could be based on the standard deviation obtained byhistorical observations (with more weight given to recent observations).It could be based on implied volatilities of options that have justtraded. Or we could use a combination of historical and impliedvolatilities to provide some balance between long and short-run trends.”In no manner, does this reference suggest an instrument, nor a means fortrading on the basis of realized volatility over a fixed time period.

Likewise, Whaley, R. E. (1993), “Derivatives on Market Volatility:Hedging Tools Long Overdue,” Journal of Derivatives (Fall) shows a waythat the CBOE could trade options on volatility on the S&P 100. Theresult of this research was the creation of a so-called “VolatilityIndex (VIX).” Yet, this index is based upon implied volatility. Impliedvolatility is derived from an options pricing model using the currentlytraded option premium to infer (or imply) the market's expectation ofthe future volatility. Since 1993, while being continuously calculatedand quoted, no contracts or instruments have been created or traded onthis index.

Neuberger, A. (1994), “The Log Contract,” Journal of PortfolioManagement (Winter), pp. 74-80, actually teaches away from the instantinvention by mentioning (without more) a volatility-type contract, andthen dismissing the concept entirely as “inflexible” and “easilymanipulated.” Instead, this reference proposes trading the Log Contract,which is merely a futures contract based upon calculating the log of thefutures price.

Other indices have emerged that further demonstrate a need for theinstant invention. The German Futures & Options Exchange (DTB),presented a volatility index similar to the VIX, called the VDAX whichis calculated from the implied volatilities of the options on the DAXindex. The VDAX began trading on Dec. 5, 1994.

Also, in 1995, The Austrian Futures and Options Exchange (OTOB)announced a volatility index on its Austrian Traded Index (ATX) forcalls and puts. In or about 1995, over-the-counter volatility swapsbegan trading. In November 1996, Volx became the first volatilityfutures, but it was based on the implied and historical volatility ofthree European stock indices: FTSE 100, DAX, and Sweden's OMX. InJanuary 1998, Volax, another volatility futures began trading on the3-month implied volatility of the DAX. None of these attempts at tradingvolatility have been successful, and they together demonstrate the longfelt need in the industry, and huge potential, for a standardizedvolatility instrument.

In terms of volatility instruments, although the concept of a contracton historical volatility was mentioned in Brenner and Galai [1989] andactual volatility again in Neuberger [1994], no one has heretoforetraveled the path of determining and designing an exchange-tradablecontract based upon realized volatility. Rather, it would appear thatthe academic community has focused on implied volatility and will notconsider any alternative.

Concepts and theories for derivatives on implied volatility have apedigree and basis in mathematics and options theory. However, theseindices appear useless as a trading vehicle. According to Brenner, M.and Dan Galai (1997), “Options on Volatility,” Option-Embedded Bonds,Irwin Publishing, Chapter 13, “[w]hile the concept of interpolating astandardized 30-day, at-the-money option from traded options is simple,the implementation can be quite complicated.” Although it is feasible totrade on implied volatility, it is unlikely that such trading would haveany serious following. Indeed, no analysis has been performed todetermine whether trading on implied volatility would even appeal tomarket participants, or what they would find useful. For a contract tobe successful, it has to be understandable by more than just a few ofthe most sophisticated players. Unfortunately, few traders willunderstand all of the math, option theory, averaging, adjustments forweekends, rolling, interpolation, extrapolation, limitations, andassumptions possessed by a contract on implied volatility.

Even if an army of educators descended upon the globe to make sureeveryone understood completely the concept of trading on impliedvolatility, there would nonetheless remain a number of problems.

Problem 1 Settling to Implied Volatility

Suppose an exchange begins trading a futures contract on an index thatsettles to implied volatility. What would participants be trying todetermine? Of course, they would try to forecast the final settlementprice. But what is the final settlement price? By definition, the finalsettlement price is the implied volatility index. But, impliedvolatility is the market's estimation of future volatility. So, if finalsettlement is to be an estimate of the future, then what, if anything,could possibly be forecast before the final settlement? The forecastwould be of an estimation. In other words, market participants would betrying to guess where the future guess of volatility would be. Thiscauses the participant to guess at a doubly intangible result. Thevariability in such guesses would demonstrate the stark need for anactual or definite determination. A problem possessed by this and allvolatility designed indices prior to the volatility contracts andinstruments described herein, has been in trying to make the index agood forecast of future volatility instead of permitting the market tomake the forecast and designing the underlying as the item forecasted.

Problem 2 Manipulation

Nueberger [1994] dismisses the mere idea of a contract settling toactual volatility because of the likelihood of market manipulation, andthus teaches away from the invention herein. Arguably, however, it wouldbe immensely easier to manipulate the implied volatility calculation atone specific moment (expiration) than to manipulate the closing futuresprice over an extended period.

Also, just because there is an ability to manipulate a market does notmean that there would be an advantage, and hence a desire, to do so.Many hedge funds have enough “firepower” to double or triple the priceof oats, rough rice, broiler chickens, or just about every option tradedon any contract. However, beyond the legal implications, there is noevidence that any such funds would ever attempt such a maneuver becausesuch activity invariably leads to large losses when the opposite,liquidating transaction is performed. Thus, risk of manipulation is notfactually supportable.

Neuberger [1994] also assumes that a long volatility trader would seekto “manipulate” the closing price of the underlying in such a way thatthe calculated volatility would be higher. However, this referenceutterly ignores the fact that the short volatility trader, who wouldhave an opposing desire, would then seek to “manipulate” the closingprice to be lower. The balance thereby achieved is suggestive of anantithetical conclusion to the one that this reference offers. Instead,the conclusion that is reached is that manipulation, an inherent risk inevery market, is no greater or different than when volatility is traded.

Moreover, even if manipulation could be shown to be profitable andlegally permissible, the exchanges for trading in such instruments wouldlikely employ countermeasures. For example, the degree of difficulty inmanipulating a price series increases in exponential proportion to thenumber of samples that are taken. Thus, instead of daily settlementreadings, exchanges could perform half-day or even hourly readings. Sucha significant increase in readings would chill, or more likely fullyprevent, any such possibility of manipulation.

Problem 3 Settling to a Continuous X-Day Implied Volatility

Supposedly, one of the main reasons for considering an impliedvolatility contract was to provide option market makers with a viablehedging vehicle. In this respect, the volatility index methodology failsto achieve that goal. The implied volatility contract's design wouldeffectively hedge this exposure for only one specific day—in the VIXcase, 30 days from expiration. The problem here is that the marketmaker, when delta hedging, has bought or sold implied volatility, butwill receive or pay, respectively, actual volatility. Supposedly, themarket maker has traded implied volatility and now wants to hedge. Hisor her needs would now center on hedging actual volatility. The solutionas discussed herein is based on realized volatility, so it would be amuch better match for this risk.

Problem 4 Attempting to Trade Options on a Contract that has NoUnderlying Market

An option without a tradable underlying would severely limit marketmakers' abilities to hedge (as has been contemplated by the CBOE for theVIX). The result would be wider spreads and lower volume, which wouldyield even wider spreads and lower volume, until the market dies. Onecould argue that a similar situation exists in the S&P 100 options pitright now (one of the most liquid markets in the world). But this is notentirely correct. There are many other very highly correlated vehiclesfrom which to hedge. Before contemplating options, exchanges must listan underlying. Accordingly, for any volatility instrument to succeed,it, too, must be based upon a listed underlying.

By way of background, U.S. Pat. No. 6,016,483 to Rickard, et al. shows amethod and apparatus for automated opening of options exchanges.Formulation and trading of risk management contracts is shown in U.S.Pat. No. 5,970,479 to Shepherd. Analysis of derivative securities isshown in U.S. Pat. No. 5,692,233 to Garman. A game concerning financialfutures is shown in U.S. Pat. No. 4,588,192 to Laborde. Negotiableinstruments are patentable, as shown by U.S. Pat. No. 6,014,454 toKunkler (see, e.g., claims 32 through 44).

In short, none of the prior art teaches or suggests the instantvolatility instruments disclosed and claimed herein.

It is thus an object of the instant invention to provide standardized,tradable financial instruments for listing on regulated andnon-regulated exchanges, based on an underlying, that settle to acalculated value of market return fluctuations over some designated timeframe.

SUMMARY OF THE INVENTION

The various features of novelty which characterize the invention arepointed out with particularity in the claims annexed to and forming apart of the disclosure. For a better understanding of the invention, itsoperating advantages, and specific objects attained by its use,reference should be had to the drawings and descriptive matter in whichthere are illustrated and described preferred embodiments of theinvention.

The foregoing objects and other objects of the invention are achievedthrough a financial instrument (also called a “contract”), exchange, andmethod based upon the realized volatility in the price of an underlying.Such volatility contracts have a creation date, a term expiring at anexpiration date, and a settlement price at the expiration date definedas “S_(vol)”, in accordance with the formula:S_(vol)={R_(t) ₁ ,R_(t) ₂ ,R_(t) ₃ , . . . , R_(t) _(n) }wherein:

-   -   S_(vol)≧0    -   n>1        and

-   t=each of a series of observation points from 1 to “n”;

-   R_(t)=return of the underlying based upon each of the observation    points in time “t_(n)”; and

-   n=total number of observations within the term.    The term is selected from the group consisting of days, months,    quarters and years. The settlement price is annualized based upon an    approximate total number of periods in a calendar year. The    observation points are taken daily, and approximate total number of    periods is selected from the group consisting of 245 to 262, and    preferably 252. R_(t) is selected from the group consisting of:

$R_{t} = {\ln\left( \frac{M_{t}}{M_{t - 1}} \right)}$$R_{t} = \left( \frac{M_{t} - M_{t - 1}}{M_{t - 1}} \right)$wherein:

-   M_(t)=mark-to-market price at time “t”; and-   M_(t−1)=mark-to-market price at the time immediately prior to time    “t”, at time “t−1”    The settlement price is determined in accordance with the following    formula:

$S_{vol} = {{\sqrt{\frac{P}{n}{\underset{t = 1}{\sum\limits^{n}}R_{t}^{2}}}\mspace{20mu}{or}\mspace{14mu} S_{vol}} = \sqrt{\frac{P}{n - 1}{\underset{t = 1}{\sum\limits^{n}}\left( {R_{t} - \overset{\_}{R}} \right)^{2}}}}$wherein:

-   P=approximate number of trading periods in a calendar year, and each    observation point “t” is taken at the same time, and-   R=mean of all R_(t)'s.

In accordance with the instant invention, a Volatility Contract (“Vol”)has been designed to be an exchange-tradable instrument similar in manyways to a futures contract. (Volatility Contract, Vol Contract, Vol andall combinations, including abbreviations, of associated contracts witha specified time frame are trademarks of Event Capital Management Corp.(www.eventcm.com). Use is by permission only.) However, instead of acontract based on the direction of prices, a Vol is based on thefluctuations of prices, or volatility in prices, over a certain timeperiod. In other words, it is based on the realized or actual volatilitythat the underlying instrument displays. Trading in the instantinstruments will significantly assist market participants in reducingthe volatility risks of the underlying. Likewise, it should beappreciated that one of ordinary skill in the art, after comprehendingthe teachings set forth herein, will well recognize that a VolatilityContract can be created on any market, and that such creation will fallwithin the spirit and claims of the subject invention.

Vol Contracts are the missing link in the current realm ofexchange-traded derivatives. It is generally recognized that futurestrade based only on direction of the underlying, while options tradebased on both direction and volatility of the underlying. Vol Contractswould trade based purely on volatility. Such Contracts should give riseto a plethora of hedging methods, speculative strategies, and arbitrageopportunities. As shown herein, Vol Contracts overcome the pitfalls inprior attempts to trade volatility. Such prior attempts have been inerror in trying to make the underlying predictive, instead of making itthe item to be predicted.

In accordance with the invention, a Volatility Contract is anexchange-tradable financial instrument. Volatility Contracts wouldsettle to a calculated value of market return fluctuations over somedesignated time frame. To quantify these price fluctuations, theinvention coins a calculated term known as realized volatility.Realized, historical, actual, and future volatilities all refer to thesame concept: the fluctuations in price level of the underlying over aperiod. The only difference is whether the period occurs in the past(historical volatility), the future (future volatility), ornon-specified (realized or actual volatility).

While there can be no perfect way of measuring realized volatility,there nonetheless must be a standard for an exchange-tradableinstrument. The final settlement is determined by one of many formulas,some of which have been outlined above. The preferred embodiment is tocalculate realized volatility based upon the annualized zero-meanstandard deviation of continuously compounded daily price returns. Whilethis method is preferred, other methods of such calculation will fallwithin the spirit and scope of the claimed invention.

A Vol, therefore, is a regulated or non-regulated exchange-tradableinstrument that would settle to the realized volatility of a specificunderlying, over a specified period of time, regardless of the exactformula used to measure the volatility or the sampling period employed.

Volatility Contracts in accordance with the subject invention can bebased on any underlying. Essentially, if a futures or an option could betraded on an asset or instrument, then a Vol could as well. For example,Bridge/CRB identifies close to 700 active futures markets all over theworld. There are presently five equity options exchanges, and aboutfifty exchanges that trade in options through the world. VolatilityContracts could be made available on any or all of them or on anyyet-to-be-listed derivatives market. Also, any listed stock, unlistedstock, physical commodity, physical asset, basket, index, currency,currency swap, treasury instruments, interest rates, market indices andcommodities, and the like are all potential candidates.

Exchanges may list just a couple Vol Contracts, initially: a 1-month Vol(Monthly Vol, M-Vol, or Vol₁) and a 3-month Vol (Quarterly Vol, Q-Vol,or Vol₃). For agricultural products, a 12-month Vol (Annual Vol, A-Vol,Vol₁₂) could be added as well. Listing an A-Vol on most financials wouldnot be needed because participants could achieve the same volatilityexposure by executing a “strip” of Quarterly Vols (similar to the wayEurodollars are strung together). It would not make sense to “strip”together agricultural products because successive contracts have nomathematical arbitrage between them. Listing of intervening monthsprobably would not be needed and, in fact, may be detrimental to thehealth of the market.

As stated, Vol is similar to a futures contract, where marketparticipants try to determine the final expiration value during much ofits life. During the realized volatility period, the contract's valuewould become more and more certain as final settlement approaches.Trading a Vol while in the realized volatility period can be consideredsimilar to the manner in which agricultural futures now trade in thedelivery month. In other words, the Vol Contract would cease to be apure anticipatory vehicle during its realized volatility period.

Other features of the present invention will become apparent from thefollowing detailed description considered in conjunction with theaccompanying drawings. It is to be understood, however, that thedrawings are designed solely for purposes of illustration and not as adefinition of the limits of the invention, for which reference should bemade to the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, wherein similar reference characters denote similarelements through the several views:

FIG. 1 is a systematic overview of the stages of creation and trading ofthe financial instrument in accordance with the subject invention;

FIG. 2 is a graphical comparison of three volatility contracts having adifferent term against futures and options;

FIG. 3 is a graphical representation of the term structure ofvolatility; and

FIG. 4 is a graphical representation showing price differentials basedupon root mean squared and mean of volatility contracts.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In accordance with the subject invention, FIG. 1 shows the four keyelements of the method and system of the instant invention. Inparticular, box 2 is directed to the creation of Vol Contracts basedupon Realized Volatility, the time during a trading period thatobservations “t” are taken, an annualization factor “P”, a formula forthe calculation of Realized Volatility, and an identified exchange forlisting the contract for trading. After creation, Vol Contracts aretraded on the exchange as shown in box 4, during the anticipatoryperiod, and a price determined by the market. Trading continues duringthe realized volatility period shown by box 6, during which the marketdetermines the price, and information necessary to determine RealizedVolatility becomes more known as the time approaches expiration of thecontract. Trading thereafter continues and eventually ends at box 8 whenexpiration occurs. Upon expiration, all open contracts settle to thecalculated value of Realized Volatility. This is the final settlementprice for the contract.

Greater comprehension can be had by consideration of the followinghypothetical example. Hypothetically, a certain exchange has acash-settled futures contract on an index that begins trading onJanuary 1. There are the following instruments trading: a Decemberfutures, options, and a 3-month Vol that all expire on December 31.

Analysis commences by determining the manner in which these instrumentssettle. Futures will settle to the index price on the final day oftrading. Options will settle to the differential between the strikeprice and the final settlement price of the underlying futures (or zeroif that result is negative). The 3-month Vol will settle to the realizedvolatility of the underlying (based upon the predetermined formula) forthe period from the close on September 30 through the final settlementof the futures on December 31.

Next in the analysis is a determination of the manner in which theseinstruments trade. Reference should be had to the diagram shown in FIG.2. Throughout the life of the futures contract, the market will beforecasting where the index price will end on December 31. For options,the goal is two-fold: option traders are anticipating the finalsettlement price (as futures traders are so doing); but also, they aremaking a forecast on the volatility that the underlying will go on todisplay from the current moment until expiration. The Vol₃ traders willbe forecasting the expected volatility of the December futures for theentire fourth quarter. Similar to options, the market will be trying toforecast the exhibited volatility of the underlying in the future. But,unlike options, the time frame being anticipated is fixed. In this case,for the first 9 months, Vol will be a pure anticipatory vehicle. Duringthe last three months of its life, information needed to settle thecontract will become more and more known.

Next is a determination of the nature of traders and users of suchinstruments. Investment banks and option market makers take on largeamounts of volatility risk as a by-product of their dynamic process ofdelta hedging. Delta hedging, also called delta-neutral hedging, is adynamic process of neutralizing directional market exposure by tradingin the underlying according to a schedule determined by an optionpricing model. The OTC options market is estimated at $13 trillion(exchange-traded options would be in addition to that figure). Whilethis product is designed for regulated or non-regulated exchanges, muchof this OTC option risk should find Vol contracts useful in reducingthis volatility risk. Neuberger [1994] stated that “ . . . over 80% ofthe hedging error that remains after delta-hedging is due to anincorrect forecast of the volatility over the life of the option.Delta-hedging reduces hedge errors by a factor of five; volatilityhedging could potentially reduce hedge errors by a further factor offive.” Assuming the validity of this statement, Volatility Contractsthen are necessary, and will likely be quite liquid.

In addition to these hedgers with direct volatility risk, there is aclass of hedgers that may find that their business could have problemswhen volatility changes. The most obvious example would bemulti-national corporations. In this case, a foreign exchange ratechange may help one part of the company while hurting another. If thisis the case, then the real risk is in exchange rates changing, not onthe direction of those changes. Definitionally, this is the veryvolatility captured and traded by the instant Vol Contracts.

Speculator are another group of users. Employment of the instant Volcontracts will provide hedge fund managers and commodity tradingadvisors with a whole new asset class on which to base trading programs.Individual speculators that now presumably use straddles and stranglesto “buy volatility” or “sell volatility” will be able to gain directvolatility exposure.

Full understanding is best had by comparison of Vol Contracts as taughtherein to futures and options.

Similarity to Futures

Vol Contracts in accordance with the preferred embodiment of the subjectinvention are similar to futures contracts in the following ways:

The profit/loss profile is linear (unlike an option);

Settlement is by cash, the same as cash-settled futures;

Market price will change based on supply and demand;

A performance bond will be necessary for both longs and shorts;

The realized volatility period for Vol Contracts and the delivery monthfor commodities are periods for which both Vol Contracts and futurescease to function as true anticipatory vehicles; and

Potentially, one could also trade options on Vol Contracts.

Similarity to Options

Vol Contracts in accordance with the preferred embodiment of the subjectinvention are similar to options in the following ways:

Each has an underlying;

Exchange-traded Vol Contracts will probably expire at the same time asthe options—not necessarily when the underlying futures contract expires(spot, equities, indices, etc. do not expire)—to allow option marketmakers the closest possible hedging vehicle.

Dissimilarity to Futures

Vol Contracts in accordance with the preferred embodiment of the subjectinvention, are dissimilar to futures in the following ways:

They do not settle to spot or some index;

The contract value is based on a calculation of the underlying's periodprice returns over a specific time frame, not just one final price atexpiration; and

The performance bond might be different for long and short positions.

Dissimilarity to Options

While a standard option's terminal value is based on the underlying'sprice on the day of expiration, Vol Contract in accordance with thepreferred embodiment, are based on the realized volatility of theunderlying over many days. In a way, a Vol Contract's expiration valueis similar to that of an exotic option known as an Asian option (orAverage Rate Option), traded in over-the-counter markets, where thefinal settlement price is determined by averaging several intermediatesettlement prices.

There are no sensitivities—delta, gamma, theta, kappa (vega), rho.

Calculation of Realized Volatility

There are a number of formulas that could be employed to measure therealized volatility associated with a particular underlying, withoutdeviation from the letter and spirit of the subject invention. There aremany reasons for both using, and not using, any particular calculation.However, one formula quantifies the annualized standard deviation ofcontinuously compounded returns, as follows:

$\sqrt{\frac{P}{n - 1}{\underset{t = 1}{\sum\limits^{n}}\left( {R_{t} - \overset{\_}{R}} \right)^{2}}}$Where:

$R_{t} = {{Ln}\left( \frac{M_{t}}{M_{t - 1}} \right)}$(each R_(t) is the continuously compounded return for one time period)Ln=Natural logarithmM_(t)=Mark-to-market priceM_(t−1)=Mark-to-market price one period prior to the aboveR=mean of all R_(t)'s.n=Number of observationst=An index to count each observation up to the maximum at nP=Number of periods in a year

It should be appreciated that observations are taken, and then summed,in accordance with the formula. A standard for the number of periods ina year should be used, and the amount annualized in accordance withindustry standards, to allow comparison between contracts of differenttime frames. Otherwise, confusion would result on the part of investorswondering the exact number of trading days in a year—which could varydepending on the calendar and the number of holidays in a particularcountry. For example, the Nikkei index trades in Singapore, Chicago, andJapan. Accounting for the time difference, the three should have thesame volatility, because they are based on the same index. However, justbecause of local holiday differences, the index trades a differentnumber of days in each location. Unless a standard period is selectedthe same contract would settle to different values. Also, it would be atrivial calculation to adjust the results for local differences.

While the foregoing formula may be employed, the preferred formula isdifferent in that it has a zero mean. Demeterfi, K., E. Derman, M.Kamal, and J. Zou (1999), “More Than You Ever Wanted To Know AboutVolatility Swaps,” Quantitative Strategies Research Notes, Goldman Sachs& Co. (March) states “the zero mean is theoretically preferable, becauseit corresponds most closely to the contract that can be replicated byoptions portfolios.” Applying these principals novelly to the instantinvention, if the zero mean is chosen, then the n−1 term becomes justn—because a degree of freedom has been removed.

Also, it does not make logical or intuitive sense to force thestatistical measure of standard deviation to conform to the markets.Doing so would imply that the trend exhibited is the “certainty” andthat it should be removed, so that the real risk could be measured. Forexample, if a market rises every day by exactly 1% for one month, theformula above would evaluate the one-month volatility as 0%. If the nextmonth the same market fell by 1% each day, its one-month volatilitywould be 0%. But, the two-month volatility for this market would bealmost 16%! Clearly, zero plus zero should not equal 16. The preferredembodiment is as follows:

$S_{vol} = \sqrt{\frac{P}{n}{\underset{t = 1}{\sum\limits^{n}}R_{t}^{2}}}$The variables in this formula are as stated hereinabove. The advantagesare as stated. Additionally, it should be observed that this formula issimpler, and such simplification would help to promote widespread use.

In terms of design considerations, it should be appreciated that everyaspect of Vol's design is directed toward simplicity. A successfulmarket needs speculators, hedgers, and market makers. A contractdesigned only for hedgers probably will not work. Market makers will notmake a “reasonable” market if there is no tradable underlying.Speculators will not trade if they do not understand the rules. It isbelieved that a successful Vol Contract will make option markets spreadstighter bringing more liquidity to the option market, which would bringmore volume to the underlying and then back to the Volatility Contract,thereby benefitting them both.

In terms of the numbers of different types of such volatility contracts,three are preferred. (It should be appreciated that any number orvariation may be used without deviation from the spirit or scope of theinvention.) It is anticipated that only three Vols need to be listed foreach underlying in agriculturals, and two Vols for financials—Vol₁,Vol₃, and Vol₁₂ for agriculturals; Vol₁ and Vol₃ for financials.Longer-term Vols, such as life of contract, would be of diminished useto hedgers and speculators as time to expiration lengthens. Long-runvolatility varies little from its long-run average. Hedgers would not beinterested in protecting from such minimal risk; speculators would findlittle opportunity, for the reasons shown in FIG. 4.

As shown in FIG. 4, if the variability in volatility is greater theshorter the time to expiration, why not have a 2-week Vol, 1-week Vol,3-day Vol, 2-day Vol, etc., etc.? Because such additional contractswould not be needed and could actually be detrimental to the health ofthe market. The reasons are twofold: First, additional contracts coulddisperse the potential volume, increasing market spreads. Second,shorter-term hedges could be created from longer-term contracts. Take,for instance, a trader wanting to hedge an option sold with 45 calendardays left to expiration. Neither a 1-month Vol (with 15 days to gobefore the start of the Realized Volatility period) nor 3-month Vol(being 45 days into the Realized Volatility period) appear to be amatch. But, Vol₃ would actually be a good match. For example, if thefirst 45 days yielded a realized volatility of 10%, and the next 45 daysturns out to be 15%, then the average is 12.5%. One can easily see thattrading two contracts would give one the same dollar exposure to anexpected increase in volatility. In reality, one would not just simplyaverage the values but use a root mean squared formula. The formula isdifferent, but the concept is the same, as shown in FIG. 5.

Volatility Swaps are gaining momentum in the OTC world. In Demeterfi[1999], the formula is just the realized volatility less the priceagreed upon today times a contract multiplier. Vol is nearly as simple.The main differences are in the fixed time period and thestandardization of terms. Exchanges have always standardized itsproducts; the OTC world has always customized them. By standardizing,exchanges can concentrate volume into the “best” (most representative)example of the underlying. Of course, Vol will not be able to meet everyparticipant's volatility needs. No single contract could. But, offeringtwo or three Vols would be able to concentrate volume into the mostrepresentative examples.

Preferred Vol Contract specifications are as follows:

Contract Size:

Like volatility, Vol is quoted in annual percentage terms. In addition,the contract multiplier should be multiplied by the number of months ofthe realized volatility period. If, for instance, Japanese yen Q-Volwere last traded at 11.22% (0.1122), and the contract multiplier were$100,000, then this Volatility Contract would be valued at $33,660($100,000×0.1122×3 months). If a Japanese yen M-Vol were traded at thesame price of 11.22%, then its value would be $11,220 ($100,000×0.1122×1month). Multiplying by the number of months might aid spreads andarbitrage between the different Volatility Contracts. The contract sizewould also correspond more closely to the smaller options premiums, asexpiration approaches. The month multiplier would add little confusionamong participants. Such a design would lead to more potential use byoption traders. Also, the variability of volatility is greatest withshorter times. Therefore, longer-term contract can have larger notionalvalues without the threat of tremendous volatility changes.

Because financial products are usually higher in notional amount andlower in average volatility than commodity futures, Vol multipliers willlikely be higher for the financials than for commodities. The contractmultiplier should be standardized as much as possible to avoid confusionand aid in market acceptance. For instance, all financials might have acontract multiplier of $100,000, all agricultural products $10,000.

Tick Size

The minimum price fluctuation for financials could be 0.01% (0.0001). Ifthe contract multiplier were $100,000, then the minimum tick size wouldbe $10 for an M-Vol and $30 for a Q-Vol. For agricultural markets, theminimum may be 0.05% (0.0005) for M-Vol and Q-Vol. If the contractmultiplier were $10,000, then the minimum tick size would be $5 for anM-Vol and $15 for a Q-Vol. An A-Vol could have the same 0.01% minimum asthe financial markets, giving it a $12 tick size.

Expiration Date

Same date on which the options on the underlying expire.

Expiration Months

1-month and 3-month Vol would appear to be most useful (also a 12-monthVol for agriculturals). Others would probably not be needed and mayactually be detrimental. Sufficient study should be conducted and marketdemand should be assessed before adding additional time frames.

Settlement

Settlement should be to cash on the calculated value of realizedvolatility (daily would be the easiest to understand and corresponds tothe way most calculate historical volatility. But, hourly could be usedif manipulation risk could be proven). Then, hourly probably should onlybe contemplated for the shortest time frame contracts (hourly reading ona 12-month Vol would be “overkill.”

Performance Bond

Because of the potential for extreme moves in volatility, theperformance bond in percentage terms should be higher than for futurescontracts in general. Also, it may be prudent to charge differentperformance bond levels depending on whether the market participant islong or short (options have such a long/short differential).

Initial Listing

The Vol contract should be listed when the underlying futures or optionsare listed.

By way of a hypothetical, Table I, appended hereto, shows trading andcalculation of a Vol in accordance with the preferred embodiment of theinvention.

In summary, a Volatility Contract has been designed to be anexchange-tradable instrument based on volatility. It can be created onany instrument with linear characteristics (e.g., futures, stock, index,currency, etc.). It will provide a way for market participants tospeculate on, or hedge against, changes in perceived market risk(volatility).

The Volatility Contracts will trade in a manner similar to a futurescontract in that market participants will be trying to forecast a futurevalue. Unlike futures contracts, though, a Vol will settle to acalculated value of an underlying over some predetermined time frame(called the Realized Volatility period), as opposed to just the value atthe end of the period. A Vol will settle to the underlying's realizedvolatility. It should expire when the corresponding options expire.

Unlike current futures contracts that have differing contractmultipliers, perhaps the contract multiplier of a Vol would be mostsuccessful being standardized among groups of financials andcommodities—$100,000×Volatility×Number of months for financials;$10,000×Volatility×Number of months for agriculturals. Similarly, theformula to calculate realized volatility should also be standardized.Doing so would ensure the greatest acceptance and participation with theleast confusion among the trading community.

An index of volatility that incorporates Implied Volatility has manydrawbacks. It could be easily manipulated. It appears to have beendesigned with only market makers in mind—but fails to accommodate them.It requires market participants to estimate a future estimation—anintangible result. Previous attempts have tried to list options before aliquid, tradable underlying was available. All of these problems aresolved with the Vol as taught herein, which, in addition, should appealto a broader array of market participants.

Currently, investment banks and market makers have significantvolatility exposure with no acceptable method of hedging. Vol, as taughtherein, will finally allow for a very good hedge, although, not anexactly arbitrageable, one-for-one match (possibly on the order of afive-fold reduction in risk or more). This instrument opens up anentirely new asset class for professional asset managers andspeculators.

While there have been shown, described and pointed out fundamental novelfeatures of the invention as applied to preferred embodiments thereof,it will be understood that various omissions and substitutions andchanges in the form and details of the device illustrated and in itsoperation may be made by those skilled in the art without departing fromthe spirit of the invention. It is the intention, therefore, to belimited only as indicated by the scope of the claims appended hereto.

1. A computer implemented method for the creation and trading offinancial instruments based upon the volatility of an underlyingcomprising the following steps: (a) creating at least one volatilitycontract for a predetermined term by a computer, with said at least onevolatility contract having a predetermined formula for settlement pricebased on a realized formula, selected from the group consisting of:$\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n - 1}{\sum\limits_{t = 1}^{n}\;\left( {R_{t} - \overset{\_}{R}} \right)^{2}}}} & (1)\end{matrix}$ wherein: P=approximate number of trading periods in acalendar year, and each observation point “t” is taken at the same timein each trading period; and R=the mean of all R_(t)'s; $\begin{matrix}{S_{vol} = \sqrt{\frac{P_{hl}}{n}{\sum\limits_{t = 1}^{n}\;\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}}}} & (2)\end{matrix}$ wherein: P_(h1)=total number of trading periods in a yearwherein two observations points “h_(t)” and “l_(t)” are used, and“h_(t)” is the high price point and “l_(t)” the low price point for eachsuch trading period in that year; and R_(t)=f{h_(t), l_(t)}; and$\begin{matrix}{S_{vol} = \sqrt{\frac{P_{ohlc}}{n}{\sum\limits_{t = 1}^{n}\;\left\lbrack {{\frac{1}{2}\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}} - {\left( {{2{\ln(2)}} - 1} \right)\left( {\ln\frac{c_{t}}{o_{t}}} \right)^{2}}} \right\rbrack}}} & (3)\end{matrix}$ wherein: P_(ohlc)=total number of trading periods, whereinfour observation points “h_(t)”, “l_(t)”, “c_(t)” and “o_(t)” are used,and “h_(t)” is the high price point, “l_(t)” the low price point,“c_(t)” is the closing, last, or daily settlement price, and “o_(t)” theopening price for each such trading period; R_(t)=f{h_(t), l_(t), c_(t),o_(t)}; and $\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}\; R_{t}^{2}}}} & (4)\end{matrix}$ wherein: P=approximate number of trading periods in acalendar year, and each observation point “t” is taken at the same timein each trading period; and n=total number of observations within theterm; and R_(t)=return of the underlying based upon each of theobservation points in time “t_(n)”; and (b) trading the at least onevolatility contract at market-determined prices from creation throughthe date of expiration.
 2. The method of claim 1, further includingsetting an approximate one-month expiration for said volatilitycontract.
 3. The method of claim 1, further including setting anapproximate three-month expiration for said volatility contract.
 4. Themethod of claim 1, further including setting an approximate 12-monthexpiration for said volatility contract.
 5. The method of claim 1,wherein$S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}\; R_{t}^{2}}}$ andfurther wherein P is the approximate number of trading periods in acalendar year, and each observation point t is taken at the same time ineach trading period; n is the total number of observations within theterm; and R_(t) is the return of the underlying based upon each of theobservation points in time t_(n).
 6. The method of claim 5, wherein saidnumber of trading periods in a calendar year is standardized.
 7. Themethod of claim 6, further including setting an approximate one-monthexpiration for said volatility contract.
 8. The method of claim 6,further including setting an approximate three-month expiration for saidvolatility contract.
 9. The method of claim 6, further including settingan approximate 12-month expiration for said volatility contract.
 10. Acomputer-implemented method for the creation and trading of financialinstruments based upon the volatility of an underlying, comprising thefollowing steps: (a) creating a volatility contract for a predeterminedterm using a computer, said computer computing a settlement price basedon a realized formula for said volatility contract selected from thegroup consisting of: $\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n - 1}{\sum\limits_{t = 1}^{n}\;\left( {R_{t} - \overset{\_}{R}} \right)^{2}}}} & (1)\end{matrix}$  wherein P=approximate number of trading periods in acalendar year, and each observation point “t” is taken at the same timein each trading period; and R=mean of all R_(t)'s; $\begin{matrix}{S_{vol} = \sqrt{\frac{P_{hl}}{n}{\sum\limits_{t = 1}^{n}\;\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}}}} & (2)\end{matrix}$  wherein P_(hl)=total number of trading periods in a year,wherein two observation points “h_(t)” and “l_(t)” are used, and “h_(t)”is the high price point and “l_(t)” the low price point for each suchtrading period in that year; and R_(t)=f(h_(t), l_(t)); and$\begin{matrix}{S_{vol} = \sqrt{\frac{P_{ohlc}}{n}{\sum\limits_{t = 1}^{n}\;\left\lbrack {{\frac{1}{2}\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}} - {\left( {{2{\ln(2)}} - 1} \right)\left( {\ln\frac{c_{t}}{o_{t}}} \right)^{2}}} \right\rbrack}}} & (3)\end{matrix}$  wherein P_(ohlc)=total number of trading periods, whereinfour observation points “h_(t)”, “l_(t)”, “c_(t)” and “o_(t)” are used,and “h_(t)” is the high price point, “l_(t)” the low price point,“c_(t)” is the closing, last, or daily settlement price, and “o_(t)” theopening price for each such trading period; R_(t)=f(h_(t), l_(t), c_(t),o_(t)); and $\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}R_{t}^{2}}}} & (4)\end{matrix}$  wherein P=approximate number of trading periods in acalendar year, and each observation point “t” is taken at the same timein each trading period; and  n=total number of observations within theterm; and  R_(t)=return of the underlying based upon each of theobservation points in time “t_(n)”; and (b) trading the createdvolatility contract at market-determined prices from creation throughthe date of expiration.
 11. The method of claim 10, wherein said numberof trading periods in a calendar year is standardized.
 12. The method ofclaim 11, further including computing said settlement price using aone-month expiration for said volatility contract.
 13. The method ofclaim 11, further including computing said settlement price using athree-month expiration for said volatility contract.
 14. The method ofclaim 11, further including computing said settlement price using a12-month expiration for said volatility contract.
 15. The method ofclaim 10, further including computing said settlement price using aone-month expiration for said volatility contract.
 16. The method ofclaim 10, further including computing said settlement price using athree-month expiration for said volatility contract.
 17. The method ofclaim 10, further including computing said settlement price using a12-month expiration for said volatility contract.
 18. The method ofclaim 10, wherein$S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}R_{t}^{2}}}$ andfurther wherein P is the approximate number of trading periods in acalendar year, and each observation point t is taken at the same time ineach trading period; n is the total number of observations within theterm; and R_(t) is the return of the underlying based upon each of theobservation points in time t_(n).
 19. The method of claim 18, whereinsaid number of trading periods in a calendar year is standardized. 20.The method of claim 19, further including computing said settlementprice using a one-month expiration for said volatility contract.
 21. Themethod of claim 19, further including computing said settlement priceusing a three-month expiration for said volatility contract.
 22. Themethod of claim 19, further including computing said settlement priceusing a 12-month expiration for said volatility contract.
 23. The methodof claim 18, further including computing said settlement price using aone-month expiration for said volatility contract.
 24. The method ofclaim 18, further including computing said settlement price using athree-month expiration for said volatility contract.
 25. The method ofclaim 18, further including computing said settlement price using a12-month expiration for said volatility contract.
 26. Acomputer-implemented method for the creation and trading of financialinstruments based upon the volatility of an underlying, comprising: (a)providing data for creating at least one volatility contract for apredetermined term in computer memory accessible to a computer dataprocessor, said data having been generated using a predetermined formulafor settlement price based on a realized formula selected from the groupconsisting of: $\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n - 1}{\sum\limits_{t = 1}^{n}\;\left( {R_{t} - \overset{\_}{R}} \right)^{2}}}} & (1)\end{matrix}$  wherein P=is the approximate number of trading periods ina calendar year, and each observation point “t” is taken at the sametime in each trading period; and   R=mean of all R_(t)'s;$\begin{matrix}{S_{vol} = \sqrt{\frac{P_{hl}}{n}{\sum\limits_{t = 1}^{n}\;\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}}}} & (2)\end{matrix}$  wherein P_(hl)=total number of trading periods in a year,wherein two observation points “h_(t)” and “l_(t)” are used, and “h_(t)”is the high price point and “l_(t)” the low price point for each suchtrading period in that year, and R_(t)=f(h_(t), l_(t)); and$\begin{matrix}{S_{vol} = \sqrt{\frac{P_{ohlc}}{n}{\sum\limits_{t = 1}^{n}\;\left\lbrack {{\frac{1}{2}\left( {\ln\frac{h_{t}}{l_{t}}} \right)^{2}} - {\left( {{2{\ln(2)}} - 1} \right)\left( {\ln\frac{c_{t}}{o_{t}}} \right)^{2}}} \right\rbrack}}} & (3)\end{matrix}$  wherein P_(ohlc)=total number of trading periods, whereinfour observation points “h_(t)”, “l_(t)”, “c_(t)” and “o_(t)” are used,and “h_(t)” is the high price point, “l_(t)” the low price point,“c_(t)” is the closing, last, or daily settlement price, and o_(t) theopening price for each such trading period; and R_(t)=f(h_(t), l_(t),c_(t), o_(t)); and $\begin{matrix}{S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}R_{t}^{2}}}} & (4)\end{matrix}$ wherein P=approximate number of trading periods in acalendar year, and each observation point “t” is taken at the same timein each trading period;  n=total number of observations within the term; and R_(t)=return of the underlying based upon each of the observationpoints in time “t_(n)”; and (b) creating by said computer data processorat least one volatility contract based on said provided data; and (c)trading the at least one volatility contract at market-determined pricesfrom creation through the date of expiration.
 27. The method of claim26, wherein said number of trading periods in a calendar year isstandardized.
 28. The method of claim 27, further including computingsaid settlement price using a one-month expiration for said volatilitycontract.
 29. The method of claim 27, further including computing saidsettlement price using a three-month expiration for said volatilitycontract.
 30. The method of claim 27, further including computing saidsettlement price using a 12-month expiration for said volatilitycontract.
 31. The method of claim 26, further including computing saidsettlement price using a one-month expiration for said volatilitycontract.
 32. The method of claim 26, further including computing saidsettlement price using a three-month expiration for said volatilitycontract.
 33. The method of claim 26, further including computing saidsettlement price using a 12-month expiration for said volatilitycontract.
 34. The method of claim 26, wherein$S_{vol} = \sqrt{\frac{P}{n}{\sum\limits_{t = 1}^{n}R_{t}^{2}}}$ andfurther wherein P is the approximate number of trading periods in acalendar year, and each observation point t is taken at the same time ineach trading period; n is the total number of observations within theterm; and R_(t) is the return of the underlying based upon each of theobservation points in time t_(n).
 35. The method of claim 34, whereinsaid number of trading periods in a calendar year is standardized. 36.The method of claim 35, further including computing said settlementprice using a one-month expiration for said volatility contract.
 37. Themethod of claim 35, further including computing said settlement priceusing a three-month expiration for said volatility contract.
 38. Themethod of claim 35, further including computing said settlement priceusing a 12-month expiration for said volatility contract.
 39. The methodof claim 34, further including computing said settlement price using aone-month expiration for said volatility contract.
 40. The method ofclaim 34, further including computing said settlement price using athree-month expiration for said volatility contract.
 41. The method ofclaim 34, further including computing said settlement price using a12-month expiration for said volatility contract.
 42. The method ofclaim 26, further comprising determining a standardized contractmultiplier.
 43. The method of claim 42, wherein said contract multiplieris standardized among groups of financials or standardized among groupsof commodities.
 44. The method of claim 43, wherein said contractmultiplier is standardized among groups of financials.
 45. The method ofclaim 44, wherein said standardized contract multiplier is determinedaccording to the formula:$100,000×Volatility×Number of Months.
 46. The method of claim 43,wherein said contract multiplier is standardized among groups offinancials.
 47. The method of claim 46, wherein said standardizedcontract multiplier is determined according to the formula:$100,000×Volatility×Number of Months.
 48. The method of claim 26,further comprising choosing a standardized formula to calculate realizedvolatility.
 49. The method of claim 48, wherein said standardizedformula is selected from one of said predetermined formulas forsettlement price.
 50. The method of claim 26, further comprising tradingsaid volatility contract on an exchange.